Anti-fracking activists led by a woman who says she talks to animals have distributed more than 140,000 copies of a “newspaper’’ that falsely claims a dramatic National Geographic picture of a West Virginia coal mine is a drilling site for natural gas, The Post has found.

The Flowback — The Costly Consequences of Hydrofracking, which is being distributed as an insert in 140,000 legitimate newspapers throughout New York’s gas-rich Southern Tier with help from a wealthy Manhattan-based environmental group, displays a grim color photograph of a mountaintop being destroyed by a large bulldozer under the heading “From My County to Yours, The Last Stand.’’

The photo is presented as a harrowing account by a woman named “Rose Baker’’ of alleged damage near her home caused by the controversial “hydrofracking’’ technique for drilling for natural gas.

However, J. Henry Fair, a prominent nature photographer who took the picture, and a spokeswoman for National Geographic told The Post that the photo actually portrays a coal-mining operation and not natural-gas drilling.

The picture appeared in the March 2011 issue of National Geographic illustrating an account of “mountaintop removal’’ for coal production.

The Flowback is published by Bonnie Jones Reynolds, a self-described former actress, author and adventurer who lives in Oneida County near Utica.

Reynolds repeatedly insisted when contacted by The Post that Fair’s photograph depicts a natural-gas drilling site. “They’re clearing off a mountain top to make their drill pads’’ for gas drilling, she contended.

Natural gas drilling, however, involves sending drilling bits deep into the earth and not ripping open mountaintops.

Fair told The Post that he had licensed the use of his photo to The Flowback on condition that the picture be identified as related to coal mining.

“I don’t know why they’d use that image like that, since my images always go out identified as to what they are, and that is obviously not a hydrofracking image,’’ said Fair.

Reynolds, author of a novel, “Magdalen,’’ that seeks to debunk some Christian teachings, claims on her Web site to be able to communicate directly with animals.

She says that, with the help of a friend, “I learned of, and began to practice, Interspecies, or Animal Communication, which is based . . . on the realization that telepathy is the language of the universe.’’

Reynolds said The Flowback is backed by the Sustainable Markets Foundation, which is headed by Jay Halfon, a former executive director of the state Trial Lawyers Association and the New York Public Interest Research Group.

Sustainable Markets, Reynolds said, accepts tax-deductible contributions on behalf of The Flowback, keeps 5 percent for itself and passes the rest on to her.

So far, she said, she has recouped about $7,000 of the estimated $40,000-plus cost of the publication.

Sustainable Markets received more than $4.3 million in contributions for the fiscal year ending Aug. 31, 2011, according to disclosure information filed with the New York Attorney General’s Office.

Halfon did not return calls seeking comment.

The Flowback’s misuse of Fair’s photograph is being cited by public officials and pro-drilling advocates as just one example of what they say are the widespread misrepresentations by anti-frackers who are seeking to frighten local residents and put pressure on Gov. Cuomo not to permit gas drilling to go forward.